Loss Landscape Engineering Via Data Regulation on Pinns

Gopakumar, Vignesh; Pamela, S.; Samaddar, Debasmita

doi:10.2139/ssrn.4280307

Cited by 3 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We will also be looking into methods of quantifying the uncertainty associated with the surrogate models and into AL pipelines that can facilitate the entire surrogate ecosystem. With the FNO for camera data, we are currently working on extending the utility across more plasma shots with a more diverse line of sights, across multiple campaigns while exploring the utility of state space models for longer predictions [47]. The work will be looking at including various control signals, to help improve the performance of the real-time predictive emulator for the MAST Tokamak, performing longer forecasting.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Plasma surrogate modelling using Fourier neural operators

Gopakumar,

Pamela,

Zanisi

et al. 2024

Nucl. Fusion

Self Cite

View full text Add to dashboard Cite

Predicting plasma evolution within a Tokamak reactor is crucial to realizing the goal of sustainable fusion. Capabilities in forecasting the spatio-temporal evolution of plasma rapidly and accurately allow us to quickly iterate over design and control strategies on current Tokamak devices and future reactors. Modelling plasma evolution using numerical solvers is often expensive, consuming many hours on supercomputers, and hence, we need alternative inexpensive surrogate models. We demonstrate accurate predictions of plasma evolution both in simulation and experimental domains using deep learning-based surrogate modelling tools, viz., Fourier Neural Operators (FNO). We show that FNO has a speedup of six orders of magnitude over traditional solvers in predicting the plasma dynamics simulated from magnetohydrodynamic models, while maintaining a high accuracy (MSE ≈ 10−5). Our modified version of the FNO is capable of solving multi-variable Partial Differential Equations (PDE), and can capture the dependence among the different variables in a single model. FNOs can also predict plasma evolution on real-world experimental data observed by the cameras positioned within the MAST Tokamak, i.e., cameras looking across the central solenoid and the divertor in the Tokamak. We show that FNOs are able to accurately forecast the evolution of plasma and have the potential to be deployed for real-time monitoring. We also illustrate their capability in forecasting the plasma shape, the locations of interactions of the plasma with the central solenoid and the divertor for the full duration of the plasma shot within MAST. The FNO offers a viable alternative for surrogate modelling as it is quick to train and infer, and requires fewer data points, while being able to do zero-shot super-resolution and getting high-fidelity solutions.

show abstract

Section: Conclusion and Discussionmentioning

confidence: 99%

Plasma surrogate modelling using Fourier neural operators

Gopakumar,

Pamela,

Zanisi

et al. 2024

Nucl. Fusion

Self Cite

View full text Add to dashboard Cite

show abstract

Stiff-PDEs and Physics-Informed Neural Networks

Sharma

Evans

Tindall

et al. 2023

Arch Computat Methods Eng

View full text Add to dashboard Cite

In recent years, physics-informed neural networks (PINN) have been used to solve stiff-PDEs mostly in the 1D and 2D spatial domain. PINNs still experience issues solving 3D problems, especially, problems with conflicting boundary conditions at adjacent edges and corners. These problems have discontinuous solutions at edges and corners that are difficult to learn for neural networks with a continuous activation function. In this review paper, we have investigated various PINN frameworks that are designed to solve stiff-PDEs. We took two heat conduction problems (2D and 3D) with a discontinuous solution at corners as test cases. We investigated these problems with a number of PINN frameworks, discussed and analysed the results against the FEM solution. It appears that PINNs provide a more general platform for parameterisation compared to conventional solvers. Thus, we have investigated the 2D heat conduction problem with parametric conductivity and geometry separately. We also discuss the challenges associated with PINNs and identify areas for further investigation.

show abstract